Crousaz, Jean-Pierre De

(b. Lausanne, Switzerland, 13 April 1663; d. Lausanne, 22 February 1750)

theology, philosophy, mathematics.

The second son of Abraham de Crousaz and Elisabeth Françoise Mayor, Crousaz belonged to one of the oldest and most noble families of Lausanne, which was then ruled by Bern. Destined at first for a military career by his father, who was a colonel, he eventually obtained permission to study philosophy and Reformed theology at the Academy of Lausanne and then at the Academy of Geneva. At the age of nineteen he went to Leiden and to Rotterdam, where he met the philosopher Pierre Bayle, and from there to Paris. Returning home in 1684, he commenced a theological career, married Louise de Loys, by whom he had three sons and four daughters, and gave private lessons in ancient languages and in the sciences. In 1700 Crousaz became a professor of philosophy and mathematics at the Academy of Lausanne; in his classes he abandoned the traditional use of Latin in favor of French. He was elected rector in 1706 and held this position for three more terms.

Crousaz’s existence was arduous: he was a minister; besides his large family, he had in his home boarders, sons of foreign and local noblemen, for whose education and instruction he was responsible; and he wrote books, such as the treatise Logique (which first appeared in two volumes, then underwent numerous alterations and had many editions—the fourth, in 1741, reached six volumes) and the Traité du beau (first in one volume, then in two). Receptive to all the intellectual currents of the age, a great correspondent, and a virulent polemicist, Crousaz poured into his writings, which he continued to produce throughout his life, all of his immense knowledge and enriched them with reflections and comments that are still of interest.

Mysterious intrigues, tenacious jealousies, and a growing hostility annoyed Crousaz and wounded his pride, although it must be admitted that humility and resignation were certainly not the dominant traits in his character. Having decided to leave Lausanne, he accepted a chair of philosophy and mathematics at the University of Groningen, where he stayed from September 1724 until March 1726 with his wife, two of his daughters, and a large retinue. He then accepted a call from the house of Hesse-Kassel to direct the education of the young heir, Prince Frederick. Crousaz had acquired a solid pedagogical reputation through his Nouvelles maximes sur l’education des enfants, published at Amsterdam in 1718, and especially through the Traité de l’education des enfants, published in two volumes at The Hague in 1722.(Rousseau had read these two works before writing Émile.)His self-esteem flattered by the titles “counselor of the court” and “governor of the prince,” Crousaz began a new life that, despite many obligations, left him leisure for his own work-especially since his family had returned to Lausanne. During this period he wrote Examen du Pyrrhonisme, a large work in which he refutes the philosophy of Bayle. The stay at Kassel lasted until 1733, when Crousaz was seventy years old; the landgrave of Hesse then granted him a life pension.

He returned to the Academy of Lausanne, where he once more held the chair of philosophy, a post that, thanks to his exceptional health, he did not relinquish until 1749, a year before his death. In this last prolific period he wrote De l’esprit humain, a harsh critique of Leibniz’s preestablished harmony, which presupposed a determinism denying free will. (Mme. du Chatelet wrote him a long letter, dated 9 August 1741, defending Leibniz.) Before the end of his long life Crousaz had the satisfaction of following the brilliant scientific career of his grandson Philippe de Loys de Chéseaux (1718–1751). Previously, upon returning from Kassel, he had the pleasure of finding his eldest son, Abraham, as rector of the Academy of Lausanne.

During the first half of his life Crousaz was a follower of Cartesianism, but he later became a defender of the ideas of Newton. It appears, however, that in each case his choice was dictated solely by philosophical and moral arguments, since he placed philosophy, theology, and pedagogy above mathematics and physics. His attacks on Leibniz, moreover, were directed only against the Théodicée, for the simple reason that he saw in this system a danger to religion. He had furnished proof of this courageous attitude in his youth while at the Academy of Lausanne, during the period when the teaching of Cartesianism was suspected of undermining orthodoxy.

As for his scientific work, Crousaz was certainly prolific, even prolix, and his treatises on elementary mathematics must have been of some interest and utility in his time. They offer, however, little that is really original; style is often neglected, with a great many repetitions; and the calculations contain errors. In analysis the work that made him famous is the Commentaire sur l’analyse des infiniment petits, a large quarto volume of 320 pages, with four plates, which appeared in 1721—three years after the work of l’Hospital, the contents of which Crousaz examines step by step. Long, superfluous passages and excessively elementary detail result in a certain lack of balance in the exposition, in which, nevertheless, one can find new examples. Crousaz had fully assimilated infinitesimal calculus, and he no doubt taught it correctly to his students. Despite its errors and insufficiencies, his book proves this, as does the welcome accorded it by contemporary scientists, Johann I Bernoulli excepted. Indeed, on 15 July 1722 the latter wrote Crousaz a long, very harsh letter filled with criticisms and more or less veiled reproaches. Bernoulli states, however (which is at least curious), that he has read only the preface and the preliminary discourses; he thus allows one to infer that he did not find his name in these pages. The reproach is justified, but if Bernoulli had continued reading, he would have found, on page 303, his name and some kind remarks about himself.

In any case, it is certain that this book contributed in great part to the nomination of Crousaz, in 1725, as associate foreign member of the Académie des Sciences of Paris. He had already received from this academy, in 1720, first prize in the annual competition for a memoir on the theory of movement. Regarding this work, Johann I Bernoulli criticized him (in the letter mentioned above) for being too Cartesian and for having, like Descartes, made “the essence of bodies consist in extension alone and that of movement in the successive application of their surfaces to the surfaces of contiguous bodies.” Crousaz was also three times (1721, 1729, 1735) a laureate of the Académie des Sciences of Bordeaux for his memoirs on the causes of elasticity, on the nature and propagation of fire, and on the different states of matter. In December 1735 he was elected a member of that academy.

Crousaz was also a great letter writer. Some 1,800 letters sent or received by him are preserved at Lausanne, and others are at Geneva, Basel, Paris, London, Leiden, Kassel, and elsewhere; they are almost all unpublished. Among his correspondents were Réaumur, Abbé Nollet, Mairan, Maupertuis, Jacques Cassini, Fontenelle, Bernoulli, and Maclaurin. With Réaumur he obviously discussed natural history, particularly certain shellfish found near Neuchåtel; with Nollet, it was electricity; Mairan was his closest confidant; to Maclaurin he addressed, in 1721, a memoir dealing with optics that, revised, was presented to the Academy of Bordeaux in 1736 under the title “Propagation de la lumière.” The secretary of this academy, Sarrau, announced his agreement with the Cartesian conclusions proposed by Crousaz.

Long called “the celebrated professor,” Crousaz appears to have had an encyclopedic mind—a mind representative of his age, of his country, and of Europe in the eighteenth century. His merit, if one accepts the éloge delivered by Grandjean de Fouchy, “seems to have been less excellence and superiority in a certain genre than universality of knowledge and of literary talents.”

BIBLIOGRAPHY

I Original Works. Crousaz’s scientific writings are Réflexions sur l’utilité des mathématiques et sur la manière de les étudier, avec un nouvel essai d’arithmétique démontrée (Amsterdam, 1715); La géométrie des lignes et des surfaces rectilignes et circulaires, 2 vols. (Amsterdam, 1718; Lausanne, 1733); Commentaire sur l’analyse des infiniment petits (Paris, 1721); Discours sur le principe, la nature et la communication du mouvement (Paris, 1721); De physicae origine, progressibus ejusque tractandae methodo… (Groningen, 1724); De physicae utilitate dissertatio philosophica (Groningen, 1725); Essai sur le mouvement, où l’on traitte de sa nature, de son origine…(Groningen, 1726); Traitè de l’algèbre (Paris, 1726); Dissertation sur la nature, l’action et la propagation du feu (Bordeaux, 1729); and Dissertation sur la nature et les causes de la liquidité et de la solidité (Bordeaux, 1735).

II. Secondary Literature. The following, listed chronologically, deal with Crousaz or his work: “Éloge de M. de Crousaz,” read 14 Nov. 1750, in Grandjean de Fouchy, Éloges des Académiciens, I (Paris, 1761), 100–122; Rudolf Wolf, Biographien zur Kulturgeschichte der Schweiz, II (Zurich, 1859), 57–70; Eugène Secrétan, Galerie suisse, Biographies nationales…, I (Lausanne, 1879), 591–599; Henri Perrochon, “Jean-Pierrre de Crousaz,” in Revue historique vaudoise (1939), 281–298; Suzanne Delorme, À propos du bicentenaire de la mort de Jean-Pierre de Crousaz: Ses relations avec l’Académie royale des sciences (Paris, 1954); Jacqueline E. de La Harpe, Jean-Pierre de Crousaz et le conflit des idées au siècle des lumières (Geneva, 1955), which is indispensable for the life literary and philosophical works of Crousaz and contains a complete list of his works; and Marianne Perrenoud, Inventaire des archives Jean-Pierre de Crousaz (Lausanne, 1969). A thorough study of his scientific work has yet to be published, and the same is true of his scientific correspondence.

Pierre Speziali